Question

If A = `[(3, x),(0, 1)] and "B" = [(9, 16),(0, -y)]`find x and y when A² = B

Answer 1

Given
A = `[(3, x),(0, 1)] and "B" = [(9, 16),(0, -y)]`find x and y when A² = B
Now, A² = A x A
= `[(3, x),(0, 1)] xx [(3, x),(0, 1)]`

= `[(9, 3x + x),(0, 1)]`

= `[(9, 4x),(0, 1)]`
We have A² = B
Two matrices are equal if each and every corresponding element is equal.
Thus `[(9, 4x),(0, 1)] = [(9, 16),(0, -y)]`
⇒ 4x = 16 and 1 = –y
⇒ x = 4 and y = –1.